The present disclosure generally relates to electric power systems and disturbance localization in electric power system.
Severe electromechanical disturbances in a power system, such as generator outage and load shedding, can significantly affect the system dynamic behaviors and put the system stability under threat. Therefore, it is important to perform disturbance detection and localization to understand the nature of the disturbance and to maintain a stable operation of the power system.
Disturbance detection may be enabled by installing a number of sensors at different locations in the power system. The electrical parameters of the power system, such as voltage and current, measured by the sensors may then be aggregated to monitor the disturbances and dynamic behaviors of the system. The fundamental of disturbance detection is that large disturbances typically cause severe deviations in voltage and frequency. Such dynamics have propagation characteristic that varies in time and space. However, due to the low sampling rate of the data recorded by conventional supervisory control and data acquisition (SCADA) system, historically, an accurate real time disturbance detection and localization has not been easy to achieve.
With the development of sensor technology, synchrophasor-based wide-area measurement system (WAMS) provides real-time awareness of power system dynamics. For example, based on high resolution data recorded by phasor measurement units (PMUs), dynamic characteristics of electrical parameters during different disturbances, e.g., short-circuit tripping, generator tripping, and load reduction, have been investigated. Correlations between disturbance features (such as disturbance location, type, and severity) and typical characteristics of corresponding frequency dynamics have been studied at length. Other methods dedicated to the improvement of disturbance identification, such as offline hierarchical clustering and hybrid state estimators, have also been studied.
Conventional disturbance localization methods typically include two steps. The first step is to obtain response times of PMUs and the second step is to estimate the location of the disturbance from the response times. To obtain response times, for each PMU, most methods calculate a time delay of arrival (TDOA) based on when its frequency or phase angle measurement exceeds a predefined threshold. The disturbance location may then be estimated by using a least square optimization to minimize the estimated distance error as in equation
                              min          ⁢                                    ∑                              i                =                1                            n                        ⁢                                          [                                                                            (                                                                        φ                          i                                                -                                                  φ                          d                                                                    )                                        2                                    +                                                            (                                                                        χ                          i                                                -                                                  χ                          d                                                                    )                                        2                                    -                                                                                    v                        2                                            ⁡                                              (                                                                              t                            i                                                    -                                                      t                            d                                                                          )                                                              2                                                  ]                            2                                      ⁢                                  ⁢                              s            .            t            .                                                  ⁢                          φ                              m                ⁢                                                                  ⁢                i                ⁢                                                                  ⁢                n                                              <                      φ            d                    <                      φ                          m              ⁢                                                          ⁢              a              ⁢                                                          ⁢              x                                      ⁢                                  ⁢                              χ                          m              ⁢                                                          ⁢              i              ⁢                                                          ⁢              n                                <                      χ            d                    <                      χ                          m              ⁢                                                          ⁢              a              ⁢                                                          ⁢              x                                      ⁢                                  ⁢                              0            <                          t              d                        <                          t              i                                ,                      ∀                          i              ∈                              {                                  1                  ,                  2                  ,                  …                  ⁢                                                                          ,                  n                                }                                                                        (        1        )            In equation (1), n denotes the number of PMUs used to estimate the disturbance location, (φ, χl) and (φd, χd) respectively denote Lambert projection coordinates of the ith PMU and the real disturbance location, ν denotes the propagation speed of the electromechanical wave, td denotes the start time of the disturbance and ti denotes the wave-front arrival time of ith PMU.
Although extensive studies have been carried out to improve the efficiency of disturbance detection methods, performing accurate disturbance identification has proven to be challenging due to assumptions that may lead to substantial errors in estimating the disturbance location. For example, most studies assume that all buses in a power system are equipped with PMUs and that the voltage and frequency at each bus are free of noise. Most studies also assume that the propagation speed of a disturbance is identical and constant in every direction, regardless of the changes in network topology and/or load conditions of the system. However, these assumptions do not always hold true.
Therefore, the inventors recognized a need in the art for systems and methods for accurately and reliably determining the location of a disturbance in an electric power system.